Topics in Multidimensional Signal Processing: Geometrical Representations and Optimal Sampling

May 5, 2008
Time: 2:00pm-3:00pm
EE Conference, 1306 Mudd
Speaker: Yue M. Lu, Swiss Federal Institute of Technology Lausanne (EPFL), Switzerland

Abstract

Multidimensional signal processing is not only a beautiful and intriguing topic in signal processing research, but also a subject of high practical impact, with its applications found in many scientific and engineering disciplines as well as in our daily lives. This talk presents my work on several topics in multidimensional signal processing. First, I will discuss the problem of finding good signal representations. The basic question is very simple: given a class of signals (e.g. natural images), how to find a transform (i.e. basis expansion) such that the signals can be more efficiently represented in the transform domain? Such efficient representations are important tools in signal processing, and lie at the heart of many modern signal enhancement and compression algorithms. I will present one constructive approach to the above problem, which is based on multidimensional filter banks. I will show how a careful arrangement and iteration of some basic signal processing operations can lead to new representations that can effectively exploit the inherent geometrical structures of multidimensional data in a robust and computationally efficient way.

Next, I will describe my work on the sampling problem, whose fundamental goal is to capture a continuous-time function with a set of samples of this function. A cornerstone result is of course Shannon's sampling theorem, which ensures the perfect reconstruction of a bandlimited function from a sufficiently dense set of its samples. An interesting question, especially in multidimensional cases, is how to find the optimal set of locations where we take the samples, with optimality determined by the corresponding sampling density (the lower the better). Instead of adopting the usual geometrical approach to this optimal sampling pattern design problem, I will describe a Fourier analytical viewpoint, which leads to purely computational solutions.Finally, I will briefly outline some of my ongoing work on the sampling and processing of spatial-temporal signals obtained by wireless sensor networks. I will describe the challenges posed by the distributed nature of the sampling process, and show how it is possible to overcome these limitations by exploiting the spatial-temporal correlation (i.e. underlying "physics") of the unknown signals.

Speaker Biography

Yue M. Lu received his Ph.D. degree in electrical engineering from the University of Illinois at Urbana-Champaign in 2007. He was a Research Assistant at the University of Illinois at Urbana-Champaign, and has worked for Microsoft Research Asia, Beijing, China and Siemens Corporate Research, Princeton, NJ. He is now with the Audio-Visual Communications Laboratory at the Swiss Federal Institute of Technology Lausanne (EPFL), Switzerland. His research interests include signal processing for sensor networks; the theory, constructions, and applications of multiscale geometric representations for multidimensional signals; image and video processing; and sampling theory.

He received the Most Innovative Paper Award of IEEE International Conference on Image Processing (ICIP) in 2006 for his paper (with Minh N. Do) on the construction of directional multiresolution image representations, the Best Student Presentation Award of the SIAM Southeast Atlantic Section Conference in 2007, and the Student Paper Award of IEEE ICIP in 2007.


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